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April 05, 2006


Alex Skiles

Hey Shieva,

I've been thinking a bit about the "at-at" theory of velocity, too, for this paper I'm drafting on vectorial properties. So, keep the posts like these coming!

Re: Your counterexample. There might be a simple (or simplistic?) response at hand for the proponent of the "at-at" theory. Suppose in both cases, we were to cut a notch in whatever fills region R1 at time T1, and then let both systems evolve. In the second case, there would be no notch in whatever fills region R2 at T2. But in the first case, there would be a notch in both regions at T1. Now, couldn't the proponent of the "at-at" theory appeal to these sorts of considerations in order to differentiate the two cases?

Alex Skiles

The second-to-last line of the previous line should read as follows (paying attention to the *-*):

<< But in the first case, there would be a notch in both regions at *T2.* >>

What this should make clear is that the difference between the two cases is *not* a kinematic one, so any theory of velocity should be able to differentiate the two cases. (Though of course, and oddly enough, what I wrote *would* be accurate in the case of backwards time travel!)


Hey Alex,

Good to hear from you - I hope things are going well at Notre Dame!

Regarding your response, I'm not yet seeing how it'll help the At-At theorist. If my case is possible, the account as commonly stated is false. Here's the formulation:

Necessarily, for any x, x moves iff there exist spaces s1 and s2, and times t1 and t2, such that s1 is distinct from s2, t1 is distinct from t2, and x is at s1 at t1 and at s2 at t2.

(There are questions about how to understand the 'at' in the account, and I argue in the paper that the most plausible way to understand it is as 'wholly at', or at least, 'has a temporal part wholly at'. It then gets a bit messier, because I need to describe temporal parts in a way that allows them to be multilocated (I argue that we need that, too). But anyway, the idea is straightforward enough.)

The considerations you appealed to seem to be outside the scope of what the above account can take as relevant to whether any given object moves.

In the paper, I'll discuss a response some may be tempted toward: keep the spirit of the account while avoiding these worries, by relativising motion to regions. It's not so unnatural, after all, since we relativise other properties to regions to avoid the problem of spatial intrinsics for spatially multilocated entities (for a discussion of the problem of spatial intrinsics, see (among other sources) Hud Hudson's 2006 book, The Metaphysics of Hyperspace). One may think that by relativising to regions, they can sneak in the extra considerations the At-At account seems to be overlooking, because those considerations will determine (or at least, partially determine) which regions we relativise to. I think this won't work, but that's an argument I'll have to leave for a future post!

Alex Skiles

Hey Shieva,

A few questions/comments:

First: Think of my suggestion as a modification of the "relativizing motion to regions" response, where now we're using intrinsic properties of the region occupiers to fix the kinematical facts, rather than the regions themselves.

Second: Now, technically you're right that for the proponent of the "at-at" theory, these considerations are "beyond the scope" of her main account. But so what? She can appeal to whatever she needs in order to differentiate the two cases, as long as it doesn't involve talking about truly instantaneous velocities and the like.

Third: No proponent of the "at-at" theory would say that simply being located in distinct spatiotemporal regions suffices for motion, basically because spatiotemporal multilocation is insufficient to guarantee that whatever is multilocated at these regions has a definite velocity. So I'm curious: From whom are you taking this formulation of the "at-at" theory?

Fourth: I'm not sure from where your intuitions about the two cases are coming. Why should we think that Case #1 involves motion? (Would we want to count *forward* time travel as motion, too?) And why should we think that Case #2 involves no motion at all?

Jonathan Ichikawa

Hey Shieva, I'm Jonathan. I've been reading your blog for a couple of years. I used to be more active in commenting than I have been of late. I just wanted to say hello and let you know that I'm transferring to Rutgers this fall (following Ernie Sosa from Brown). I'm looking forward to it. So: see you around!

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